Chaire Galaxies et Cosmologie

Coupling between the structures d h d kand the dark sector

Françoise Combes

Relation large-scale structures– dark energy

The Universe: homogeneous and isotrope at the beginningLarge-scale structures today are highly contrastedEffect on space-time dynamics? « back-reaction »Average density to compute the metricAverage density to compute the metricNon commutativity, Einstein equations are non-linear

Galaxy clusters as cosmological testsIn addition to BAO, and gravitational lensesS d d l d diStandard ruler and distance measurementUniversal baryon fraction

Growth rate of structures, affected by the progressive domination of dark energyp g gyTest of modified gravity

The Copernic PrincipleHypothesis, quasi philosophical, that our Universe ishomogeneous and isotropeg p

One of the bestconfirmation: the diffusemicro-wave background

~10-5

Large-scale structures of the local Universe

4Nearby clusters and superclusters

SDSSSDSS

~106

5600Mpc~2 billion lyr

Density of structures in the UniverseSolar system 10-12 g/cm3

Milky Way 10-24 g/cm3

Local Group 10-28 g/cm3

G l l t 10 29 / 3Galaxy cluster 10-29 g/cm3

Supercluster 10-30 g/cm3Supercluster 10 g/cm

Density of photons (3K) 10-34 g/cm3

Density of baryons (b) 5 10-31 g/cm3

Critical density (=1) 10-29 g/cm3

6 ~1030 on Earth!

Smoothing of inhomogeneities

The smoothing of inhomogeneities modifies considerably the structure of Ei i i hi h liEinstein equations, which are non-linearThe two operations do not commuteSolve the equations then smooth ≠ smooth then solve the equations

GTG 8Solve the equations then smooth, ≠ smooth then solve the equations

The inhomogeneities introduce then a reaction with respect smoothing,e o oge e es oduce e a eac o w espec s oo g,a term of “back-reaction” in the right-hand side of the equationThere is no reason for the effective tensor energy-momentum Twith the back-reaction, to satisfy the usual conditions P>-/3,even though the original T satisfied themThe smoothing is useful to avoid singularitiesThe smoothing is useful to avoid singularities.The back-reaction term could lead to an accelerated expansionEven from a fluid with positive or null pressurep p

Acceleration due to inhomogeneitiesAcceleration due to inhomogeneitiesHomogeneous model Inhomogeneous model

3

h

V

3h ha V

Hh h hH a a

h i x ?h iH H

May be, or may-be not!

The principle of inhomogeneitiesThe principle of inhomogeneities•Friedmann–Lemaître–Robertson–WalkerInhomogeneous model

FLRW, ,G x t G t G x t

Inhomogeneous model

FLRW00 00 00

, ,

, 8 ,G t G x t GT x t

Homogeneous flat model,Ei i d Si P 0

2

008 3

3 8a G G

G

Einstein-deSitter P~0

003 8a G

d i / ( )< > domain = -4G/3 (eff + 3Peff)

Kolb, et al 2006, 2011Buchert, 2000, 05, 07

Average at large-scaleAverage at large-scale

1/3 3a V V V d x h

• Average over a large volume VD:

0 D D D DD

a V V V d x h • Corresponding Hubble constant :

13

DD D

D

aHa

4Da G

• Equations of effective evolution:

RQ Diff t f eff eff

2

4 33

8

D

D

a G pa

G

eff 16 163

D DD

RQG GRQ

Different from l’equation ofstate

eff8

3D

D

a Ga

eff33

16 16D D

RQpG G

p w

• Backreaction: 22 223 2D DD D

Q

Advantages of inhomogeneitiesAdvantages of inhomogeneities• No need to add a 5th force!

•No need to modify gravity, keep general relativityd f di i•No need of extra dimensions

•Explains why dark energy is becoming significant only now•(5Gyr ago), while the contrast in structures develops with time• Negligible at T~400 000 yrs

•Magic? However we still need a proof that / is sufficient•Modifies the zero mode and the scale factor•Modifies the zero mode, and the scale factor

Perturbations larger than the horizonPerturbations larger than the horizon• The largest observable perturbation has the scale of Hubble radius

todaytoday

Hubble Radius (5Gpc)z= 2 1018 4000 0 5

10-32s 40 103yr 5 109yrz 2 10 4000 0.5

Lesgourgues 2006

10-32s

Toy model from Nambu-Tanimoto (2005)• The basis: flat universe LTB Lemaître-Tolman-Bondi, solution of

Einstein equationsq• Contains a region of positive curvature (c), and one negative• When the dense region collapses, then on average the expansion g p , g p

of the ensemble accelerates

LDeceleration

r0

open

closed

open

t/(oL3)closed

Acceleration Also Mansouri 2005, Alnes et al 2006

Estimation of Green & WaldG = 8G/c4 T

• Green & Wald, 2011, 13, 16: introduction of a computation methodWi h h h (0)

G 8G/c T

• With hypotheses: g = g(0) + << 1, but not the derivatives g(0) is not solution of Einstein

eq ations C r at re of g at scale of H bble radi sequations -- Curvature of g at scale of Hubble radius

I h iti L << R(H bbl )Inhomogeneities on L << R(Hubble)Average over the scales L << D << R b k ti i ti f th d f 1% back reaction: variations of the order of 1%Always positive, traceless tensor

Justification: the perturbations are not far from Newtonian (v non l ti i ti ) ith li ti t bl k h lrelativistic), with linear equations, except near black holes

True for Einstein, bit not for f(R)

But a smooth background metric…Estimation without approximation ( expansion shear)

Shows a term with a non-zero traceShows a term with a non zero trace

The equations are undetermined. What is the dependence on time q pof QD?

Could QD become large enough to accelerate the expansion? P bl th ll f t t f tiProblems as soon as the collapse of structures form caustics

Voids are important and must be taken into account

Buchert et al 2015, Kolb et al 2016

Computations from Bardeen et al (2007)Even in the toy model from Nambu-Tanimoto (2005)The density contrast give rise to causticsAll the mass is found in a shell (LTB non valid)All the mass is found in a shell (LTB non valid)Less deceleration, but no acceleration of expansion

S scaleCurvature

S scalefactor

R/SR/S

RayonThe average has no longer any senseNewtonian approx is valid, relativistic effects negligible

Rayon

In summary The perturbations beyond horizon provide no acceleration

The inhomogeneities at small scale could “renormalise” the large The inhomogeneities at small scale could renormalise the large scale acceleration on average (+3P <0)

The smoothing of perturbations below horizon raises problems, and should be done properly

In a frame comoving with the matter flow unless unreliableresults

An effect which should be quantified, even it cannot explain the dark energydark energy

The debate keeps open !The debate keeps open !

Clarkson et al 2011

Some tests are possibleM f di tMeasure of distances

Curvature of geodesics ExpansionCurvature and distance coupled in standard, not in LTBAlso k independent of zTests on the BAO ruler, Supernovae, SDSS surveys

Measure of redshift evolution(Uzan et al 2008 Liske et al 2008)

dz/dt

(Uzan et al 2008, Liske et al 2008)

Or else w(z) requires also H’(z)Or else w(z), requires also H (z)

Simulations 20 yrs of observationsof 10 QSO with ELT, H=8km/s

z

Baryonic acoustic peak Power

Waves detected todayIn the distribution of baryonsy

50 000 galaxies in SDSS

Separation

Eisenstein et al 2005

19

A simple perturbation

Creates a depression

Sound wave at c /√3 Sound Horizonat recombination

R 150MpcR~150Mpc

Gala iesGalaxies

In the over-densites

20Acoustic waves Daniel Eisenstein

Multiple perturbationsSignal reduced by therandom phasesMultiple wavesl 1% in the P(k)

Power

Daniel Eisenstein

21Separation

Expected oscillationsExpected oscillations

Not in phaseNot in phaseat small scales(velocities)( )

And 2x wavelength

Hütsi 2005Hütsi 2005

22M. White 2007

BAO: baryonic oscillationsy

Radial BAO: dr = (c/H)dz

cz/H

Radial BAO: dr (c/H)dzIn the plane of the sky: dr = DAd

Observer

D

Better than the CMB3D instead of 2D!

D

c z/H = D Alcock & Paczynski (1979)T t f th l i l t t

P ibilit t

Test of the cosmological constant

Can test the bias b

23

Possibility to determine H(z)

Can test the bias bOr = m

5/9/b

Power spectrum of matter fluctuations

Linear power spectrum

S l f h i P(k)Scale of the maximum P(k)= horizon size at the epoch ofmatter-radiation

Large scales Small

matter-radiation equivalence

50 000 yrs after the Big-Bang

f 1/3f m = 1/3

m = 3 7evm 3.7ev

The relativistic neutrinos

25

Reduce small-scale structures

Voids dominate the UniverseGalaxy clusters, 3- 15 Mpc, + network of filaments and surfaces like “walls” surrounding voidsg

The Universe is dominated by voids (60–80%) in volume, with a di t ib ti d h t i ti l (40% f th t t l l )distribution and a characteristic scale (40% of the total volume)

Voids ~40 Mpc density contrast of ~ -0 94Voids 40 Mpc, density contrast of 0.94

The statistic homogeneity scale is of 100 -150 MpcAt larger scales, the contrast < 0.4

Th i iti l t b ti lifi d b tiThe initial perturbations are amplified by acoustic wavesThe statistic homogeneity scale is near that of BAO

BAO can be considered in the linear regime

Tests of backreaction modelsBelow this scale, there can exist differential expansionsdue to inhomogeneities

Towards LeoVelocity of Local Group vs CMB = 645 km/sVsun LG 318km/s

Towards aquariusVsun-LG= 318km/sDipole of 3.31 mK

Determination of peculiar velocitiesDetermination of peculiar velocitiesVpec= cz –H0 r

Local cosmic flowsPeculiar velocities: to reach the underlying potential Vpec= cz –H0 rb, DM,

Distance indicators Tully-Fisher Tip of Red Giant branch Fl t ti f f Fluctuations of surfacebrightness Fundamental plane Fundamental plane Cepheids

The origin of the dipoleNot yet completely elucidated

Lavaux et al 2010

In which direction?

A di h id d

Dipole CMB

According to the consideredvolumes

Lavaux et al 2010

Dipole CMB

Unknown still remain

Flat Universe, k= 0m = 0.3, CDM

Obs m=0.15-0.2

Lavaux et al 2008

The dipole does not converge

2MASS galaxies in NIR, depths ofmin and max 7 and 400 Mpcp(Virgo 17Mpc, Hydra 47 Mpc,Leo > 120 Mpc)

The data analysisThe data analysisYields a value of m = 0.20m

= m0.55/b = 0.38

Bilicki et al 2011M03: Maller et al 2003E06 Erdogdu et al 2006

Simulations of the local UniverseTh b SNI i ld diff t l f HThe nearby SNIa yield a different value of H0They follow the dipole, and therefore are biased +Divergent velocities around Virgo boost H0 H0=1 76 km/s/MpcDivergent velocities around Virgo, boost H0 H0 1.76 km/s/Mpc

Hess & Kitaura 2016

Residual cosmic flow ~200km/sIn spite of the increase of the galaxy number, the residual velocityis still unexplained

Springob et al 2016Blue, green, redIncreasing volume

We live at the border of a superclusterIt contains the clusters of Virgo, Hydra-Centaurus, Pavo-IndusLaniakea in the process of dilution, dispersion (160Mpc, 1017M)

ShapleyComa

Perseus-Pisces

35Tully et al 2014

Rees-SciamaRees Sciamaeffect

The late ISW effect (in the local Universe), when it becomes

li i ll d R S inon-linear is called Rees-Sciama

In presence of the super-clusters and voids see their density contrastIn presence of , the super-clusters and voids see their density contrastdecreasingThe microwave photons get out of super-clusters bluer (morep g p (energetic) and the contrary in voids

T if h ff i l h li h lTo quantify the effect, one must simulate the light travelin the non-linear relativistic regime

ray-tracing algorithm

Relativistic simulations of differential expansionRelativistic simulations of differential expansionThe effect of inhomogeneities is simulated exactly, without the g y,smoothing approximationImpossible to account for observations, without a non-kinematicalffeffect

(1+z)obs= (1+z)expHo(1+z)pech d i li l i i i ll dWhat does not enter in peculiar velocities vpec, is called

non-kinematic effect

The underlying expansion is supposed to come from the isotropiclocal model, with an average FLRW metric, gThe CMB dipole corresponds to T/T =1.23 10-3, of the same orderOf magnitude than =v/c = 2.1 10-3, but there are residuals

Bolejko et al 2016

Simulations with the Szekeres modelThe effect of inhomogeneities (local void Great attractor) is simulatedThe effect of inhomogeneities (local void, Great attractor) is simulatedexactly, by numerically solving Einstein equationsOn the photon path effect of anisotropies on the expansionp p p p

Bolejko et al 2016Dipole Quadrupole8/h Mpc

8/h Mpc

DATA

LTB

Simulationsof BAO

Springel et al 2005

Power spectrumDM and galaxiesin the BAO regionin the BAO region(after division bythe linear CDMspectrum)

Blue: all pointsBlack: average

39

State of BAO measuresWith SDSS galaxies, 8500°2, 0.2 < z < 0.7, sound horizon rdH=96.8 + 3.4 km/s/Mpc Distances/rd compatible with CDM

H from the separation

and

Anderson et al 2014

BAO with the Ly forestIonised gas absorbants in cosmic filamentsin front of remote quasars 137 000 quasars 2.1 < z < 3.5S d h i 2 34 dSound horizon at z=2.34 : rdDA/rd 7% smallerDH/rd 7% largerDH/rd 7% largerthan CDM

Significant to 2.5

Z=2.91

Delubac et al 2015

Test of modified gravity models

Yamamoto et al 2006

42

Dvali-Gabadadze-Porrati « DGP model »

Gravitational lenses

The distance as a function of redshift depends on

Growth of structures, depends on

43Schneider 2003

Reduces the number of galaxiesgAmplification of background sourcesBy increasing their radius Conservation of surface brightnessBy increasing their radius, Conservation of surface brightnessReduction of the source density

Discrepant recent results?Hildebrandt et al 2016 KIDS: 450°2 weak gravitational lensing

15 millionsof galaxies

Discordantwith Planck-2015

Comparison of several data sets

Galaxy clusters and dark energyClusters provide different and complementary tests

On distances, fgas ~fbar is supposed universal (17%)

O h h f d k h iOn the growth of structures: dark energy has an actionopposing gravity, and limits their formationStudy as a function of zStudy as a function of z

The rate of growth probesg pmodified gravity models, at very large scales

Vikhlinin 2008

Self-similar distribution

At the centre, this is no longer, gtrue, because of cooling flowphenomena

Chandra

Morandi & Sun 2016

Constance of baryons/total ratioMgas mass of X-ray gas Mt t total mass of the galaxy cluster

gasgas M

Mf Mtot total mass of the galaxy cluster

The hot gas represents the bulk of baryons gasgal fhf 5.019.0tot

g M

The baryon fraction in clusters = universal baryon fraction

bb b is the bias factor, bbf f +f m b

fgas(1 0.19h0.5),

accounts for gas ejected at the

m

bbaryon bf

fgas+fgal=

formation epoch of the clusterDistances measured for 0.06<z<1.2 320 clusters

5.1

mod )()(

)19.01()(

zdzd

hbzf

A

refAb

gas

Mgas dA(z)2.5

Mtot dA(z) V2 R

test combined with +HST+BBNS priors

)()19.01( dh Am

Test of galaxy clustersX-ray emission of 320 galaxy clusters0.056 < z < 1.24, kT> 3 keV with the X-ray satellite Chandra

Clusters are self-similarEspecailly in outer parts

E ti f t t fEquation of state of dark energy P= w

w= -1.010±0.030

Compatible with a cosmological constant

Morandi & Sun 2016

Coma clusterX-rays, optical,

XMM‐Newton= X

X rays, optical, Sunyaev-Zeldovich

ff t (SZ)effect (SZ)

Telescope CFHT= optical

H diffHot diffuse gas107K, 13%

Galaxies: 2%

Dark matter: 85%

Two tracers of the hot gasBremstrahlung radiation

Total SZ flux, proportional to Mgas/DA(z)2

SZ effect detected by PlanckIntensity I

SPT 244 SZ d d (1 1’) Tdlny e

SPT 244 SZ detected (1.1’)ACT 91 detected (1.4’)

Planck 1653 sources (5’)1200 galaxy clusters

frequency

g y

2

ref

obsref

yydd

Advantages of clustersg

• Standard ruler, measure of distances with X and SZ: precision semilar to SNIa and BAO with some advantages

Simple physics, models and simulations The X-ray emission improves in S/N fgas : extra constraint on Ωm

fgas + CMB raise up degeneraciesg

Low systematic dispersion in fgas(z) X+SZ independent of bias and of hydrostatic equilibrium

Resistance to the gravityResistance to the gravityDark energy reduces the number and the mass of clusters

w

Vikhlinin et al 09Vikhlinin et al 09

Growth of Growth of structures

Number of clusters as a function of redshift

Test of equation ofstate of dark energy

P wP=w

ww

m

Summary

Could large-scale structures contribute to dark energy? Atwhich scale does isotropy dominate?which scale does isotropy dominate?and « back-reaction » become negligible?

Several complementaty tests of dark energy BAOW k l iWeak lensingGalaxy clustersAs standard ruler and measure of distanceAs standard ruler and measure of distanceAnd using the universal baryon fraction

Growth rate of structures, perturbed by the progressive domination of dark energy, tests of modified

itgravity